How do I export a render as a PNG with a color depth of 32 bit?
The Portable Network Graphics (PNG) format doesn't support more than 16-bit per sample in the color channel. You can use a format such as OpenEXR or Radiance HDR if you need 32-bit per sample in the color channel.

Section 4.1 Images explains this (emphasis mine):


  The reference image, which only exists conceptually, is a rectangular
  array of rectangular pixels, all having the same width and height, and
  all containing the same number of unsigned integer samples, either
  three (red, green, blue) or four (red, green, blue, alpha). The array
  of all samples of a particular kind (red, green, blue, or alpha) is
  called a channel. Each channel has a sample depth in the range 1 to
  16, which is the number of bits used by every sample in the channel.
  Different channels may have different sample depths. The red, green,
  and blue samples determine the intensities of the red, green, and blue
  components of the pixel's colour; if they are all zero, the pixel is
  black, and if they all have their maximum values (2sampledepth-1), the
  pixel is white. The alpha sample determines a pixel's degree of
  opacity, where zero means fully transparent and the maximum value
  means fully opaque. In a three-channel reference image all pixels are
  fully opaque. (It is also possible for a four-channel reference image
  to have all pixels fully opaque; the difference is that the latter has
  a specific alpha sample depth, whereas the former does not.) Each
  horizontal row of pixels is called a scanline. Pixels are ordered from
  left to right within each scanline, and scanlines are ordered from top
  to bottom. A PNG encoder may transform the source image directly into
  a PNG image, but conceptually it first transforms the source image
  into a reference image, then transforms the reference image into a PNG
  image. Depending on the type of source image, the transformation from
  the source image to a reference image may require the loss of
  information. That transformation is beyond the scope of this
  International Standard. The reference image, however, can always be
  recovered exactly from a PNG datastream.


Section 11.2.2 IHDR Image Header explains precisely what bit depths are allowed depending on the type of information that is stored.


  Bit depth is a single-byte integer giving the number of bits per
  sample or per palette index (not per pixel). Valid values are 1, 2, 4,
  8, and 16, although not all values are allowed for all colour types.
  See 6.1: Colour types and values.
  
  Colour type is a single-byte integer that defines the PNG image type.
  Valid values are 0, 2, 3, 4, and 6.
  
  Bit depth restrictions for each colour type are imposed to simplify
  implementations and to prohibit combinations that do not compress
  well. The allowed combinations are defined in Table 11.1.


Table 11.1 — Allowed combinations of colour type and bit depth
PNG image type       | Colour type | Allowed bit depths | Interpretation
Greyscale            | 0           | 1, 2, 4, 8, 16     | Each pixel is a greyscale sample
Truecolour           | 2           | 8, 16              | Each pixel is an R,G,B triple
Indexed-colour       | 3           | 1, 2, 4, 8         | Each pixel is a palette index; a PLTE chunk shall appear.
Greyscale with alpha | 4           | 8, 16              | Each pixel is a greyscale sample followed by an alpha sample.
Truecolour with alpha| 6           | 8, 16              | Each pixel is an R,G,B triple followed by an alpha sample.